On Multistage Learning a Hidden Hypergraph

Learning a hidden hypergraph is a natural generalization of the classical group testing problem that consists in detecting unknown hypergraph $H_{un}=H(V,E)$ by carrying out edge-detecting tests. In the given paper we focus our attention only on a specific family $F(t,s,\ell)$ of localized hypergraphs for which the total number of vertices $|V| = t$, the number of edges $|E|\le s$, $s\ll t$, and the cardinality of any edge $|e|\le\ell$, $\ell\ll t$. Our goal is to identify all edges of $H_{un}\in F(t,s,\ell)$ by using the minimal number of tests. We develop an adaptive algorithm that matches the information theory bound, i.e., the total number of tests of the algorithm in the worst case is at most $s\ell\log_2 t(1+o(1))$. We also discuss a probabilistic generalization of the problem.Comment: 5 pages, IEEE conferenc

Magnetization Losses in Multiply Connected YBa2Cu3O6+x Coated Conductors

We report the results of a magnetization losses study in experimental multifilament, multiply connected coated superconductors exposed to time-varying magnetic field. In these samples, the superconducting layer is divided into parallel stripes segregated by non-superconducting grooves. In order to facilitate the current sharing between the stripes and thus increase the reliability of the striated conductors, a sparse network of superconducting bridges is superimposed on the striated film. We find that the presence of the bridges does not substantially increase the magnetization losses, both hysteresis and coupling, as long as the number of bridges per length of the sample is not large. These results indicate that it is possible to find a reasonable compromise between the competing requirements of connectivity and loss reduction in an ac-tolerant version of the high temperature coated conductors specifically designed for ac power applications.Comment: 19 pages, 12 figures to be published in J. Appl. Phy

Magneto-optical studies of the uniform critical state in bulk MgB2

We present a detailed magneto-optical investigation of the magnetic flux penetration in polycrystalline MgB2 slabs made by direct reaction of B and Mg. Our results unambiguously indicate a uniform, Bean critical state magnetization behavior with almost no electromagnetic granularity. From the measured magnetic flux profiles we were able to extract the temperature dependence of the critical current density Jc(T). The Jc(T) value reaches 1.8x10^5 A/cm2 at 10K and 0.12T, in good agreement with global magnetization measurements

Influence of vortex-vortex interaction on critical currents across low-angle grain boundaries in YBa2Cu3O7-delta thin films

Low-angle grain boundaries with misorientation angles theta < 5 degrees in optimally doped thin films of YBCO are investigated by magnetooptical imaging. By using a numerical inversion scheme of Biot-Savart's law the critical current density across the grain boundary can be determined with a spatial resolution of about 5 micrometers. Detailed investigation of the spatially resolved flux density and current density data shows that the current density across the boundary varies with varying local flux density. Combining the corresponding flux and current pattern it is found that there exists a universal dependency of the grain boundary current on the local flux density. A change in the local flux density means a variation in the flux line-flux line distance. With this knowledge a model is developped that explains the flux-current relation by means of magnetic vortex-vortex interaction.Comment: 7 pages, 14 figure